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Composite finite elements for elliptic interface problems


Author: Daniel Peterseim
Journal: Math. Comp. 83 (2014), 2657-2674
MSC (2010): Primary 65N30, 65N12, 35R05, 80M10
Published electronically: February 26, 2014
MathSciNet review: 3246804
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Abstract: A Composite Finite Element method approximates linear elliptic boundary value problems with discontinuous diffusion coefficient at possibly high contrast. The discontinuity appears at some interface that is not necessarily resolved by the underlying finite element mesh. The method is non-conforming in the sense that shape functions preserve continuity across the interface in only an approximate way. However, the method allows balancing this non-conformity error and the error of the best approximation in such a way that the total discretization error (in energy norm) decreases linear with regard to the mesh size and independent of contrast.


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Additional Information

Daniel Peterseim
Affiliation: Institut für Mathematik, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099 Berlin, Germany
Address at time of publication: Institut für Numerische Simulation der Universität Bonn, Wegelerstr. 6, 53115 Bonn, Germany
Email: peterseim@ins.uni-bonn.de

DOI: https://doi.org/10.1090/S0025-5718-2014-02815-9
Received by editor(s): October 25, 2010
Received by editor(s) in revised form: January 16, 2012, and February 16, 2013
Published electronically: February 26, 2014
Additional Notes: The present paper is a full version of an extended abstract presented at the 81st Annual Meeting of the International Association of Applied Mathematics and Mechanics, Karlsruhe (Germany), 2010. The work was partially supported by the DFG Research Center MATHEON Berlin through project C33.
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.